A176295 Triangle read by rows, based on the two-variable g.f. exp(x*t)*(x*(1 - 2*exp(x)) - 2*exp(x))/(1 - exp(t)) (the second of two parts).
-4, 4, 8, 2, -10, 0, 12, 0, 16, -32, -16, 32, -4, -4, 120, -120, -120, 120, 0, -96, -96, 960, -480, -864, 576, 80, 80, -1680, -1680, 8400, -1680, -6720, 3360, 0, 3840, 3840, -26880, -26880, 80640, 0, -57600, 23040, -6048, -6048, 120960, 120960, -423360, -423360, 846720, 120960, -544320, 181440
Offset: 0
Examples
Triangle begins as: -4, 4, 8; 2, -10, 0, 12; 0, 16, -32, -16, 32; -4, -4, 120, -120, -120, 120; 0, -96, -96, 960, -480, -864, 576; 80, 80, -1680, -1680, 8400, -1680, -6720, 3360; 0, 3840, 3840, -26880, -26880, 80640, 0, -57600, 23040;
References
- Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco, 1965, pp 296-298
Links
- G. C. Greubel, Rows n = 0..100 of triangle, flattened
Programs
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Mathematica
p[t_]:= Exp[x*t]*(x*(1 -2*Exp[x]) -2*Exp[x])/(1-Exp[t]); Table[Im[ CoefficientList[2*n!*(n+2)!*SeriesCoefficient[Series[p[t], {t,0,30}]/.Exp[x] -> I, n], x]], {n,0,12}]//Flatten
Extensions
Edited by N. J. A. Sloane, Jan 01 2011
Comments